Criteria for Irreducibility of mod Representations of Frey Curves
Authors:
- Nuno FreitasNFNuno Freitas
- Samir SiksekSSSamir Siksek
- 21 May 2015
- journal article
- Published by MathDoc/Centre Mersenne in Journal de Théorie des Nombres de Bordeaux
- Vol. 27 (1) , 67-76
Abstract
Let be a totally real Galois number field and let be a set of elliptic curves over . We give sufficient conditions for the existence of a finite computable set of rational primes such that for and , the representation is irreducible. Our sufficient conditions are often satisfied for Frey elliptic curves associated to solutions of Diophantine equations; in that context, the irreducibility of the mod representation is a hypothesis needed for applying level-lowering theorems. We illustrate our approach by improving on a result of [6] for Fermat-type equations of signature .
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